Surface runoff hydrograph derivation using a dynamic wave based instantaneous unit hydrograph

Rainfall-runoff models based on unit hydrographs and geomorphological instantaneous unit hydrographs have been widely used because of their simplicity and applicability. However, they are conceptual approaches, and not a reflection of physical phenomena. As an alternative, dynamic wave models have been introduced, but they are not appropriate for practical purposes because of their numerical instability and high computational cost. In this study, we present a hybrid method composed of a dynamic wave approach and instantaneous unit hydrograph (IUH) to predict surface runoff physically, stably, and instantly. We generate the S-hydrographs of a watershed using a dynamic wave model, and the IUHs of the watershed are derived by numerically differentiating the S-hydrographs with respect to time. Finally, a direct runoff hydrograph is produced through the convolution of the temporally varying rainfall excess rate and the IUHs of the watershed. A dynamic wave model is used, and therefore, only a single parameter related to friction needs to be calibrated for the S-hydrograph generation, and the nonlinearity of the rainfall-runoff process can be partially considered. From a computational perspective, the proposed method after the IUH derivation ends instantly and stably. Tests for ideal and real watersheds show good agreement between measurements and dynamic wave modelling results.